Flat surfaces that correspond to meromorphic -forms with poles or to meromorphic quadratic differentials containing poles of order two and higher have infinite flat area. We classify groups that appear as Veech groups of translation surfaces with poles. We characterize those surfaces such that their -orbit or their -orbit is closed. Finally, we provide a way to determine the Veech group for a typical infinite surface in any given chamber of a stratum.
Les surfaces plates correspondant aux -formes méromorphes ou aux différentielles quadratiques contenant des pôles d’ordre au moins deux ont une aire infinie. Nous donnons une classification des groupes apparaissant comme groupes de Veech de surfaces de translation avec pôles. Nous caractérisons les surfaces dont l’orbite sous l’action de ou est fermée. Enfin, nous déterminons le groupe de Veech d’une surface générique appartenant à une chambre donnée d’une strate.
Accepted:
Published online:
Guillaume Tahar 1

@article{AFST_2020_6_29_1_57_0, author = {Guillaume Tahar}, title = {Veech groups of flat surfaces with poles}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {57--78}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 29}, number = {1}, year = {2020}, doi = {10.5802/afst.1623}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1623/} }
TY - JOUR AU - Guillaume Tahar TI - Veech groups of flat surfaces with poles JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2020 SP - 57 EP - 78 VL - 29 IS - 1 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1623/ DO - 10.5802/afst.1623 LA - en ID - AFST_2020_6_29_1_57_0 ER -
%0 Journal Article %A Guillaume Tahar %T Veech groups of flat surfaces with poles %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2020 %P 57-78 %V 29 %N 1 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1623/ %R 10.5802/afst.1623 %G en %F AFST_2020_6_29_1_57_0
Guillaume Tahar. Veech groups of flat surfaces with poles. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 29 (2020) no. 1, pp. 57-78. doi : 10.5802/afst.1623. https://afst.centre-mersenne.org/articles/10.5802/afst.1623/
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